A015423 - OEIS

%I #22 Sep 08 2022 08:44:40

%S 1,2731,14913991,54301841231,237244744338239,942314556807454559,

%T 3920970870875818419999,15935828658299317547308959,

%U 65529064844612576067331339935,267883966717492783113707839256735

%N Gaussian binomial coefficient [ n,12 ] for q=-2.

%D J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

%D M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

%H Vincenzo Librandi, <a href="/A015423/b015423.txt">Table of n, a(n) for n = 12..200</a>

%F a(n) = Product_{i=1..12} ((-2)^(n-i+1)-1)/((-2)^i-1) (by definition). - _Vincenzo Librandi_, Nov 06 2012

%t Table[QBinomial[n, 12, -2], {n, 12, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)

%o (Sage) [gaussian_binomial(n,12,-2) for n in range(12,22)] # _Zerinvary Lajos_, May 28 2009

%o (Magma) r:=12; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 06 2012

%Y Diagonal k=12 of the triangular array A015109. See there for further references and programs. - _M. F. Hasler_, Nov 04 2012

%K nonn,easy

%O 12,2

%A _Olivier Gérard_